In the art of dispensing fluidic ink objects as it applies to radial printing, there is a need to place ink objects accurately and precisely onto the spinning circular media to effectively use the mechanisms of radial printing. Radial printing, as referenced above in U.S. Pat. No. 6,264,295, in Bradshaw et al, generally includes the process of dispensing ink onto a media at a particular radius of the media and a particular angular position while the media is rotating. During the radial printing process, inks are dispensed to the rotating media in a predetermined manner based upon selection of available points in a print image and correcting for errors resulting from the Cartesian-to-polar conversion process.
FIG. 2 illustrates a radial printing system 200, as described in Bradshaw et al, used to print on circular media 210 as it rotates 214. Host computer 270 runs imaging algorithms 272 that compute, among other things, Cartesian-to-polar conversion results 254, which are imaged 280 for use by the pen control system 250. While angular position is synchronized 230 by encoder 240 the motor 260 rotates and the pen control system fires ink jet pen 220, such that ink objects 212 impinge at target radii 216 along radial axis 218 and angle 226 during rotation 214. A radial print system must accommodate continuously widening ink object dispersion with increasing radial position, necessitating the use of a polar coordinate mapping techniques. In doing so, the number of ink objects 212 printed increases proportionately with the radius, as the pen moves radially 216 outward and each increasingly larger annular ring is printed.
In conventional Cartesian printing systems, halftone screening is used to generate varying levels of intensity or to print grayscale or color images. As shown in FIG. 1, traditional halftone techniques, widely known in the art and used for conventional Cartesian printers, assume a Cartesian printing environment in which intensity or dot density varies along the X-axis 112, Y-axis 110 or the screen sampling angle 114.
As discussed in Bradshaw et al, to facilitate printing radially, all Cartesian points must be first converted to polar coordinates. However, when Cartesian halftones undergo this conversion and are used with radial printing applications, the transformed halftones (as shown in FIG. 5) yield poor results on disc media 210 and often exhibit moiré interference patterns 510˜520. The resulting moiré interference patterns during radial printing are distracting to the viewer, dominate the visage, and vary unpredictably with color, intensity, and hue. The polar conversion algorithms 272 (FIG. 2) used to prepare an image for radial printing attempts to select or sample as many qualified points from the Cartesian rendered image as possible, while adjusting for potential conversion errors. Moiré interference patterns result during Cartesian-to-polar conversion for radial printing when the polar sampling frequency beats directly with the original Cartesian halftone frequency or their harmonics. As a result, when used for radial printing applications, traditional Cartesian-based halftone techniques inherently cause moiré patterns and are thus usually not suitable for radial printing.
In view of the foregoing, halftone mechanisms which reduce or substantially eliminate interference patterns during radial printing are needed.